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arXiv:0905.2217 · Physical Review Letters

Optimizing Anharmonicity in Nanoscale Weak Link Josephson Junction Oscillators

Rajamani Vijay, Jay Deep Sau, Marvin L. Cohen, Irfan A. Siddiqi

Published Aug 19, 2009• 49 citations
arXivHTMLPDF

Abstract

We compute the current phase relation for superconducting weak links, with dimensions comparable to the zero temperature coherence length, connected to two and three dimensional superconducting electrodes. Our results indicate that 50-100 nm long aluminum nanobridges with three dimensional banks have sufficient anharmonicity for realizing low noise amplifiers and quantum bits. Such weak link junctions thus present a practical new route for realizing sensitive quantum circuits with potentially higher quality factor than tunnel junction devices due to the absence of a lossy oxide layer.

DOI
10.1103/physrevlett.103.087003

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We compute the current phase relation for superconducting weak links, with dimensions comparable to the zero temperature coherence length, connected to two and three dimensional superconducting electrodes. Our results indicate that 50-100 nm long aluminum nanobridges with three dimensional banks have sufficient anharmonicity for realizing low noise amplifiers and quantum bits. Such weak link junctions thus present a practical new route for realizing sensitive quantum circuits with potentially higher quality factor than tunnel junction devices due to the absence of a lossy oxide layer.
We investigate unshunted dc superconducting quantum interference devices (SQUIDs) consisting of aluminum nanobridges of varying length L contacted with (two dimensional, or 2D) and (three dimensional, or 3D) banks. 3D nanobridge SQUIDs with L≤150 nm (approximately four times the superconducting coherence length) exhibit ≈70% critical current modulation with applied magnetic field, approaching the theoretical limit for an ideal short metallic weak link. In contrast, 2D nanobridge SQUIDs exhibit significantly lower critical current modulation. This enhanced nonlinearity makes 3D nanobridge Josephson junctions well suited to optimize sensitivity in weak link SQUID magnetometers as well as realize ultralow-noise amplifiers and qubits.
We present the driven response at T=30 mK of 6 GHz superconducting resonators constructed from capacitively-shunted three-dimensional (3D) aluminum nanobridge superconducting quantum interference devices (nanoSQUIDs). We observe flux modulation of the resonant frequency in quantitative agreement with numerical calculation and characteristic of near-ideal short weak-link junctions. Under strong microwave excitation, we observe stable bifurcation in devices with coupled quality factor (Q) ranging from 30–3500. Near this bias point, parametric amplification with >20 dB gain, 40 MHz bandwidth, and near quantum-limited noise performance is observed. Our results indicate that 3D nanobridge junctions are attractive circuit elements to realize quantum bits.
We report the realization of multilayer three-dimensional nanobridge Josephson junctions based on Nb/NbN and Nb/TiN superconducting stacks fabricated using electron-beam lithography and chlorine-based dry etching. In this architecture, a high-resistivity nitride layer defines the geometrical weak link, while the top Nb layer sets the overall critical temperature and film quality of the stack. This multilayer design enables engineering of the superconducting gap and proximity effects without relying on focused ion beam milling or oxide tunnel barriers. The devices are successfully integrated into dc SQUIDs, demonstrating reliable circuit-level operation. By combining material selectivity with three-dimensional geometry, this platform provides a scalable route toward oxide-free Josephson junctions suitable for superconducting electronics.
We optimized a process to reliably fabricate thin Nb nanobridge weak links having a physical size comparable with Nb coherence length ξ(4.2K) ∼16 nm, controlled degraded superconductivity with respect to the electrodes, and excellent edge roughness. We then investigated the feasibility to use these nanobridges as the Josephson element for reduced footprints and efficient next-generation single flux quantum (SFQ) logic electronics. First of all, we demonstrated that in such thin Nb nanobridges, there is no thermal hysteresis in the current–voltage characteristics (IVC) that instead is usually observed in other weak links and prevents their use in SFQ electronics. We fitted the experimental IVCs of nanobridges with the resistively shunted junction model implemented with piecewise linear current–phase relation (CPR) finding a very good agreement with data. This allowed us to infer the CPR parameters and evaluate the product of critical current and normal resistance,IcRn∼mV, at varying temperatures. Using these data, we simulated the generation of voltage pulses at varying CPRs and verified that they still have a quantized area equal to the magnetic flux quantum Φ0and the productIcRnallows for speed of operationIcRN/ Φ0$\gg 100GHz.Moreover,theircriticalcurrentIc100 GHz. Moreover, their critical currentIc100GHz.Moreover,theircriticalcurrentIc\approx 100100100\mu A,comparablewiththatoftunnelJosephsonjunctions(JJs)usedinSFQelectronics,isordersofmagnitudelargerthanthermalcurrentnoiseITN=(2π/Φ0)kBTA, comparable with that of tunnel Josephson junctions (JJs) used in SFQ electronics, is orders of magnitude larger than thermal current noiseITN= (2π / Φ0)kBTA,comparablewiththatoftunnelJosephsonjunctions(JJs)usedinSFQelectronics,isordersofmagnitudelargerthanthermalcurrentnoiseITN=(2π/Φ0)kBT\approx 0.20.20.2\mu AattemperatureT=4.2K,forstableand,atthesametime,efficientoperationwithenergyperswitchofonlyEJ≈ICΦ0A at temperatureT= 4.2 K, for stable and, at the same time, efficient operation with energy per switch of onlyEJ≈ICΦ0AattemperatureT=4.2K,forstableand,atthesametime,efficientoperationwithenergyperswitchofonlyEJ≈ICΦ0\mathbin{\hbox{$\buildrel<\over {\smash{\scriptstyle \sim}\vphantom{_x}}$}} $1 aJ. To assess the potential use of these nanobridges in SFQ logic electronics with a large number of elements, we used an open-source simulation software (JSim) to simulate the behavior of a standard DC-to-SFQ converter circuit. From the simulation made by implementing the CPR inferred from experimental data, we observed that the circuit behaves exactly as intended. Our results strongly suggest that these nanobridges can be used to develop large-scale SFQ electronics with several advantages over tunnel JJs. The reduced footprint, just one-third or less than standard tunnel JJs, and simplified fabrication process, with only 2 steps involved against typically ∼20 for tunnel JJs, could allow for a better fabrication tolerance, higher control on operation parameters, higher circuit density, and easier integration with other technology platforms. These characteristics could be very appealing also to replace tunnel JJs in quantum technology devices like transmon qubits and superconducting parametric amplifiers.
Josephson junctions are the basis of superconducting qubits, amplifiers, and magnetometers. Historically, tunnel-style junctions have been most common. However, for some applications--those requiring a small, highly transparent, all-superconducting junction--nanobridge weak link junctions may be preferable. This thesis presents extensive characterization of aluminum nanobridge Josephson junctions. The junction behavior is simulated by numerically solving the Usadel equations. These simulations are then tested and confirmed via low- and microwave-frequency transport measurements. The data confirm that nanobridge junctions approach the ideal weak-link Josephson limit.Such a near-ideal junction can be used in a superconducting quantum interference device (SQUID) to form an ultra sensitive magnetometer. This thesis presents the first nanobridge-based dispersive SQUID magnetometer. The devices show near-zero dissipation, with bandwidth and sensitivity on par with the best reported results for any SQUID-based magnetometer. These magnetometers have several flexible modes of operation, allowing for optimization of sensitivity, bandwidth, or backaction. They also provide insight into the internal dynamics of dispersive measurement with nonlinear cavities, as the magnetometer backaction depends on the bias point and can readily be measured.Nanobridge junctions also provide a useful tool for diagnosing sources of decoherence in superconducting qubits. By replacing the usual tunnel junction with a nanobridge, the contribution of the junction to decoherence processes may be probed. In particular, the interaction of nanobridge junctions with quasiparticles provides information both about the junctions themselves and about quasiparticle generation and relaxation mechanisms. This thesis reports measurements of nonequilibrium quasiparticles trapping in phase-biased nanobridge junctions. By probing the quasiparticle-induced changes in resonant frequency of a high-Q nanoSQUID oscillator, one may measure the mean distribution of trapped quasiparticles and study its temperature dependence. These measurements also provide spectroscopy of the junctions' internal Andreev states and the dynamics of quasiparticle excitation and retrapping. The work presented here demonstrates the utility of nanobridge junctions as a tool for quantifying the population and distribution of quasiparticles in a superconducting circuit.
The Josephson effect, as an example of a macroscopic quantum phenomenon, reveals itself in the three-layer heterostructures formed by two superconductors coupled by a weak link that usually consists of a 1-2 nm-thick insulating barrier.The traditional way of modelling such-systems' dynamics is based on an equivalent circuit that comprises three parallel elements: a pure superconducting element with a certain supercurrent-versus-Josephson phase difference dependence, a resistor R, and a capacitor C. In this short review, we analyse the practical problem of reducing the junction capacitance while maintaining or slightly impairing other characteristics.Some arguments are presented to explain why the capacitance should be suppressed and how it will affect performance of superconducting quantum interference devices (SQUIDs) and digital electronics circuits.As a solution for low-capacitance junctions, we propose a weak link made of an amorphous-silicon interlayer doped with nanoscale metallic drops between the two superconducting Mo-Re-alloy electrodes.